Question: $\dfrac{ 10s - 2t }{ 4 } = \dfrac{ -3s + 9u }{ 5 }$ Solve for $s$.
Explanation: Multiply both sides by the left denominator. $\dfrac{ 10s - 2t }{ {4} } = \dfrac{ -3s + 9u }{ 5 }$ ${4} \cdot \dfrac{ 10s - 2t }{ {4} } = {4} \cdot \dfrac{ -3s + 9u }{ 5 }$ $10s - 2t = {4} \cdot \dfrac { -3s + 9u }{ 5 }$ Multiply both sides by the right denominator. $10s - 2t = 4 \cdot \dfrac{ -3s + 9u }{ {5} }$ ${5} \cdot \left( 10s - 2t \right) = {5} \cdot 4 \cdot \dfrac{ -3s + 9u }{ {5} }$ ${5} \cdot \left( 10s - 2t \right) = 4 \cdot \left( -3s + 9u \right)$ Distribute both sides ${5} \cdot \left( 10s - 2t \right) = {4} \cdot \left( -3s + 9u \right)$ ${50}s - {10}t = -{12}s + {36}u$ Combine $s$ terms on the left. ${50s} - 10t = -{12s} + 36u$ ${62s} - 10t = 36u$ Move the $t$ term to the right. $62s - {10t} = 36u$ $62s = 36u + {10t}$ Isolate $s$ by dividing both sides by its coefficient. ${62}s = 36u + 10t$ $s = \dfrac{ 36u + 10t }{ {62} }$ All of these terms are divisible by $2$ $s = \dfrac{ {18}u + {5}t }{ {31} }$